The probability of successfully landing a plane using a flight simulator is give
ID: 3275281 • Letter: T
Question
The probability of successfully landing a plane using a flight simulator is given as 0.84. 14 randomly and independently chosen student pilots are asked to try to fly the plane using the simulator. Round your answers to three decimal places (e.g. 98.765).
(a) What is the probability that all the student pilots successfully land the plane using the simulator?
(b) What is the probability that none of the student pilots successfully lands the plane using the simulator?
(c) What is the probability that exactly 13 of the student pilots successfully land the plane using the simulator?
Explanation / Answer
(a) The probability of successfully landing a plane = 0.84
=> The probability that all 14 students successfully land the plane = (0.84)14
= 0.087
(b) The probability of not successfully landing a plane = 0.16
=> The probability that none of the 14 students successfully land the plane = (0.16)14
(c) The probability of successfully landing a plane = 0.84
The probability that 13 student pilots land successfully = (0.84)13
The probability that the 14th student pilot does not land successfully = 0.16
The 13 students can be chosen in 14C13 = 14 ways
=> Probability that exactly 13 students successfully land the plane
= (0.84)13 * 0.16 * 14
= 0.2322
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